45 citations · 125 across the 11 of their papers we have counts for
18 papers
Ax-Schanuel and the rank one Riemann-Hilbert correspondence
Jonathan Pila, JacobTsimerman
We prove an Ax-Lindemann theorem for the rank one Riemann-Hilbert correspondence on a smooth projective complex algebraic curve and recover a result of Simpson.
Periods in Families and Derivatives of Period Maps
Ben Bakker, Jonathan Pila, Jacob Tsimerman
Given a smooth proper family , we study the (quasi)-periods of the fibers of as (germs of) functions on . We show that they field they generate has the sam…
Ax-Schanuel and exceptional integrability
Jonathan Pila, Jacob Tsimerman
When can a primitive of a given algebraic function be con-structed by iteratively solving algebraic equations and composing withthe primitives of some other given algebraic functio…
Canonical Heights on Shimura Varieties and the André-Oort Conjecture
Jonathan Pila, Ananth N. Shankar, Jacob Tsimerman +2
The main purpose of this work is to prove the André-Oort conjecture in full generality.
Effective transcendental Zilber-Pink for variations of Hodge structures
Jonathan Pila, Thomas Scanlon
We prove function field versions of the Zilber-Pink conjectures for varieties supporting a variation of Hodge structures. A form of these results for Shimura varieties in the conte…
Independence of CM points in Elliptic Curves
Jonathan Pila, Jacob Tsimerman
We prove a result which describes, for each , all linear dependencies among images in elliptic curves of special points in modular or Shimura curves under parameterizat…